I'm guessing that what happened is that the OP was booked on two different airlines. If that was the case, it would not be Delta's fault. They wouldn't know the pax was enroute unless they had a complete itinerary and if both airlines were part of SkyTeam Alliance (Northwest, Continental). Had the OP been booked on the same airline straight through, he would have been checked in for the second flight also with boarding passes in hand for both flights.
This isn't all that uncommon -- I see it all the time on sites such as Orbitz and Expedia, and the flights may sometimes be less expensive than going with one airline.
For those finding themselves in this situation, see if it's possible for you to check in online for both of your flights. This can typically be done within 24 hours of the flight. It's not always possible, though -- I ran into this situation once last year. But I had something like 6 hours between flights (business meetings in the first city), so it wasn't an issue for me.
But back to our original story -- there's got to be more to it. What was the first airline? How much time was between flights? I hope the OP returns so that we can learn more and therefore offer some advice.